The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Authoritative sources in a hyperlinked environment
Journal of the ACM (JACM)
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Chord: A scalable peer-to-peer lookup service for internet applications
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
A scalable content-addressable network
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Parallel Algorithms for Matrix Computations
Parallel Algorithms for Matrix Computations
Global Information from Local Observation
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems
Middleware '01 Proceedings of the IFIP/ACM International Conference on Distributed Systems Platforms Heidelberg
On clusterings-good, bad and spectral
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Spectral Partitioning of Random Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Tapestry: An Infrastructure for Fault-tolerant Wide-area Location and
Tapestry: An Infrastructure for Fault-tolerant Wide-area Location and
Gossip-Based Computation of Aggregate Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Fastest Mixing Markov Chain on a Graph
SIAM Review
Speeding up algorithms on compressed web graphs
Proceedings of the Second ACM International Conference on Web Search and Data Mining
Link analysis for private weighted graphs
Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval
Brief paper: Decentralized estimation and control of graph connectivity for mobile sensor networks
Automatica (Journal of IFAC)
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A spectral clustering approach to validating sensors via their peers in distributed sensor networks
International Journal of Sensor Networks
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Distributed rating prediction in user generated content streams
Proceedings of the fifth ACM conference on Recommender systems
Hearing the clusters of a graph: A distributed algorithm
Automatica (Journal of IFAC)
Robust distributed orthogonalization based on randomized aggregation
Proceedings of the second workshop on Scalable algorithms for large-scale systems
Privacy-Preserving EM algorithm for clustering on social network
PAKDD'12 Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
Distributed QR factorization based on randomized algorithms
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Journal of the ACM (JACM)
Decentralized estimation of Laplacian eigenvalues in multi-agent systems
Automatica (Journal of IFAC)
Mixing local and global information for community detection in large networks
Journal of Computer and System Sciences
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In many large network settings, such as computer networks, social networks, or hyperlinked text documents, much information can be obtained from the network's spectral properties. However, traditional centralized approaches for computing eigenvectors struggle with at least two obstacles: the data may be difficult to obtain (both due to technical reasons and because of privacy concerns), and the sheer size of the networks makes the computation expensive. A decentralized, distributed algorithm addresses both of these obstacles: it utilizes the computational power of all nodes in the network and their ability to communicate, thus speeding up the computation with the network size. And as each node knows its incident edges, the data collection problem is avoided as well. Our main result is a simple decentralized algorithm for computing the top k eigenvectors of a symmetric weighted adjacency matrix, and a proof that it converges essentially in O(@t"m"i"xlog^2n) rounds of communication and computation, where @t"m"i"x is the mixing time of a random walk on the network. An additional contribution of our work is a decentralized way of actually detecting convergence, and diagnosing the current error. Our protocol scales well, in that the amount of computation performed at any node in any one round, and the sizes of messages sent, depend linearly on the degree of the node, polynomially on k, but not at all on the (typically much larger) number n of nodes. To achieve independence of n, the coordinates of the computed eigenvectors are held locally by the nodes to which they correspond, enabling many eigenanalyses without distributing complete global state.